Sparse matrix technique applied to topological analysis of large-scale electrical networks

1972 ◽  
Vol 92 (1) ◽  
pp. 62-70 ◽  
Author(s):  
H. Sato
Keyword(s):  
Large Scale ◽  
Sparse Matrix ◽  
Topological Analysis ◽  
Electrical Networks

Special parallel processor for lu decomposition of a large-scale sparse matrix

1987 ◽  
Vol 18 (6) ◽  
pp. 89-99 ◽  
Author(s):  
Hideki Asai ◽  
Mitsuo Asai ◽  
Mamoru Tanaka
Keyword(s):  
Large Scale ◽  
Sparse Matrix ◽  
Lu Decomposition ◽  
Parallel Processor

scholarly journals Crystal structure of a tankyrase 1–telomere repeat factor 1 complex

2016 ◽  
Vol 72 (4) ◽  
pp. 320-327 ◽  
Author(s):  
Bo Li ◽  
Ruihong Qiao ◽  
Zhizhi Wang ◽  
Weihong Zhou ◽  
Xin Li ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Large Scale ◽  
Sparse Matrix ◽  
Critical Role ◽  
Three Dimensional ◽  
Mitotic Cell ◽  
Ankyrin Repeat ◽  
Dimensional Structure ◽  
Telomere Repeat ◽  
Tankyrase 1

Telomere repeat factor 1 (TRF1) is a subunit of shelterin (also known as the telosome) and plays a critical role in inhibiting telomere elongation by telomerase. Tankyrase 1 (TNKS1) is a poly(ADP-ribose) polymerase that regulates the activity of TRF1 through poly(ADP-ribosyl)ation (PARylation). PARylation of TRF1 by TNKS1 leads to the release of TRF1 from telomeres and allows telomerase to access telomeres. The interaction between TRF1 and TNKS1 is thus important for telomere stability and the mitotic cell cycle. Here, the crystal structure of a complex between the N-terminal acidic domain of TRF1 (residues 1–55) and a fragment of TNKS1 covering the second and third ankyrin-repeat clusters (ARC2-3) is presented at 2.2 Å resolution. The TNKS1–TRF1 complex crystals were optimized using an `oriented rescreening' strategy, in which the initial crystallization condition was used as a guide for a second round of large-scale sparse-matrix screening. This crystallographic and biochemical analysis provides a better understanding of the TRF1–TNKS1 interaction and the three-dimensional structure of the ankyrin-repeat domain of TNKS.

scholarly journals Request, Coalesce, Serve, and Forget: Miss-Optimized Memory Systems for Bandwidth-Bound Cache-Unfriendly Applications on FPGAs

2022 ◽  
Vol 15 (2) ◽  
pp. 1-33
Author(s):  
Mikhail Asiatici ◽  
Paolo Ienne
Keyword(s):  
Large Scale ◽  
Sparse Matrix ◽  
Memory Systems ◽  
Graph Analytics ◽  
Matrix Vector Multiplication ◽  
Area Reduction ◽  
Cache Line ◽  
Speed Up ◽  
Memory Accesses ◽  
On Chip

Applications such as large-scale sparse linear algebra and graph analytics are challenging to accelerate on FPGAs due to the short irregular memory accesses, resulting in low cache hit rates. Nonblocking caches reduce the bandwidth required by misses by requesting each cache line only once, even when there are multiple misses corresponding to it. However, such reuse mechanism is traditionally implemented using an associative lookup. This limits the number of misses that are considered for reuse to a few tens, at most. In this article, we present an efficient pipeline that can process and store thousands of outstanding misses in cuckoo hash tables in on-chip SRAM with minimal stalls. This brings the same bandwidth advantage as a larger cache for a fraction of the area budget, because outstanding misses do not need a data array, which can significantly speed up irregular memory-bound latency-insensitive applications. In addition, we extend nonblocking caches to generate variable-length bursts to memory, which increases the bandwidth delivered by DRAMs and their controllers. The resulting miss-optimized memory system provides up to 25% speedup with 24× area reduction on 15 large sparse matrix-vector multiplication benchmarks evaluated on an embedded and a datacenter FPGA system.

The Local Singular Boundary Method for Solution of Two-Dimensional Advection–Diffusion Equation

2021 ◽  
pp. 2150041
Author(s):  
Karel Kovářík ◽  
Juraj Mužík
Keyword(s):  
Diffusion Equation ◽  
Large Scale ◽  
Sparse Matrix ◽  
Singular Boundary ◽  
Tracer Transport ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Boundary Method ◽  
Local Variant ◽  
Singular Boundary Method

This work focuses on the derivation of the local variant of the singular boundary method (SBM) for solving the advection-diffusion equation of tracer transport. Localization is based on the combination of SBM and finite collocation. Unlike the global variant, local SBM leads to a sparse matrix of the resulting system of equations, making it much more efficient to solve large-scale tasks. It also allows solving velocity vector variable tasks, which is a problem with global SBM. This paper compares the results on several examples for the steady and unsteady variant of the advection-diffusion equation and also examines the dependence of the accuracy of the solution on the density of the nodal grid and the size of the subdomain.

scholarly journals Local memory boosts label propagation for community detection

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Antonio Maria Fiscarelli ◽  
Matthias R. Brust ◽  
Grégoire Danoy ◽  
Pascal Bouvry
Keyword(s):  
Community Detection ◽  
Large Scale ◽  
Linear Time ◽  
Topological Analysis ◽  
Detection Algorithm ◽  
Label Propagation ◽  
Performance Study ◽  
Global Knowledge ◽  
Local Optima ◽  
Propagation Algorithm

Abstract The objective of a community detection algorithm is to group similar nodes that are more connected to each other than with the rest of the network. Several methods have been proposed but many are of high complexity and require global knowledge of the network, which makes them less suitable for large-scale networks. The Label Propagation Algorithm initially assigns a distinct label to each node that iteratively updates its label with the one of the majority of its neighbors, until consensus is reached among all nodes in the network. Nodes sharing the same label are then grouped into communities. It runs in near linear time and is decentralized, but it gets easily stuck in local optima and often returns a single giant community. To overcome these problems we propose MemLPA, a variation of the classical Label Propagation Algorithm where each node implements a memory mechanism that allows them to “remember” about past states of the network and uses a decision rule that takes this information into account. We demonstrate through extensive experiments, on the Lancichinetti-Fortunato-Radicchi benchmark and a set of real-world networks, that MemLPA outperforms other existing label propagation algorithms that implement memory and some of the well-known community detection algorithms. We also perform a topological analysis to extend the performance study and compare the topological properties of the communities found to the ground-truth community structure.

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